Equilibrium constant for the formation of $HI\left(g\right)$ as:

${\text{H}}_2\left(\text{g}\right)+{\text{I}}_2\left(\text{g}\right)\underset{ }{\rightleftharpoons }2\text{HI}\left(\text{g}\right)$ can be expressed as $\log k=\frac{270}{T}+\mathrm{0.4.}\text{\hspace{0.17em}\hspace{0.17em}Then\hspace{0.17em}\hspace{0.17em}}\Delta \text{G}=\_\_\_\_\_k\text{J\hspace{0.17em}\hspace{0.17em}at\hspace{0.17em}\hspace{0.17em}500K}$